document.write( "Question 767962: find all possible numbers whose sum and product are same. example 2+ 2=4 & 2*2=4, 1.5*3 = 4.5 & 1.5 + 3 = 4.5 \n" ); document.write( "
Algebra.Com's Answer #468104 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
find all possible numbers whose sum and product are same. example 2+ 2=4 & 2*2=4, 1.5*3 = 4.5 & 1.5 + 3 = 4.5
\n" ); document.write( "
\r\n" );
document.write( "Suppose x+y = xy\r\n" );
document.write( "\r\n" );
document.write( "Suppose a,b,c, and d are numbers such that\r\n" );
document.write( "\r\n" );
document.write( "x = \"a%2Fb\" and y = \"c%2Fd\"\r\n" );
document.write( "\r\n" );
document.write( "Then \r\n" );
document.write( "\r\n" );
document.write( "\"a%2Fb\"\"%22%22%2B%22%22\"\"c%2Fd\"\"%22%22=%22%22\"\"a%2Fb\"×\"c%2Fd\"\r\n" );
document.write( "\r\n" );
document.write( "\"a%2Fb\"\"%22%22%2B%22%22\"\"c%2Fd\"\"%22%22=%22%22\"\"%28ac%29%2F%28bd%29\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply every term through by bd\r\n" );
document.write( "\r\n" );
document.write( " ad + bc = ac\r\n" );
document.write( "\r\n" );
document.write( "-ac + ad = -bc\r\n" );
document.write( "\r\n" );
document.write( " ac - ad = bc\r\n" );
document.write( "\r\n" );
document.write( "a(c - d) = bc\r\n" );
document.write( "\r\n" );
document.write( "a = \"%28bc%29%2F%28c-d%29\", c≠d\r\n" );
document.write( "\r\n" );
document.write( "Choose any three numbers b, c and d, such that c≠d\r\n" );
document.write( "\r\n" );
document.write( "Choose a = \"%28bc%29%2F%28c-d%29\"\r\n" );
document.write( "\r\n" );
document.write( "Then x = \"a%2Fb\" and y = \"c%2Fd\"\r\n" );
document.write( "\r\n" );
document.write( "will be such that x+y = xy\r\n" );
document.write( "\r\n" );
document.write( "Example:\r\n" );
document.write( "\r\n" );
document.write( "Choose b=3, c=7, d=2\r\n" );
document.write( "\r\n" );
document.write( "Let a = \"%28bc%29%2F%28c-d%29\" = \"%283%2A7%29%2F%287-2%29\" = \"21%2F5\" = 4.2\r\n" );
document.write( "\r\n" );
document.write( "Then x = \"a%2Fb\" = \"4.2%2F3\" = 1.4\r\n" );
document.write( "\r\n" );
document.write( "And y = \"c%2Fd\" = \"7%2F2\" = 3.5 \r\n" );
document.write( "\r\n" );
document.write( "Then x+y = 1.4 + 3.5 = 4.9\r\n" );
document.write( "\r\n" );
document.write( "And xy = 1.4×3.5 = 4.9\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );